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This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.
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Previews available in: English
Subjects
Differentiable dynamical systems, Differential equations, Nonlinear, Nonlinear Differential equations, Systemes dynamiques, Nichtlineare Differentialgleichung, Equations differentielles non lineaires, Dynamisches System, Equacoes diferenciais, Dynamique differentiable, Equations differentielles, Gewohnliche Differentialgleichung, Sistemas dinamicos, Qa372 .p47 2001, 515/.353Showing 5 featured editions. View all 11 editions?
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2
Differential Equations and Dynamical Systems
2001, Springer
Hardcover
in English
- 3rd ed.
0387951164 9780387951164
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3
Differential Equations and Dynamical Systems
1996, Springer
electronic resource /
in English
- Second edition.
146840251X 9781468402513
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4
Differential equations and dynamical systems
1996, Springer
in English
- 2nd ed.
0387947787 9780387947785
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WorldCat
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5
Differential equations and dynamical systems
1991, Springer-Verlag
in English
0387974431 9780387974439
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Book Details
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This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles.
In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.
--back cover
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August 1, 2023 | Edited by AgentSapphire | Edited without comment. |
August 1, 2023 | Edited by AgentSapphire | remove incorrect isbn |
February 27, 2022 | Edited by ImportBot | import existing book |
July 26, 2019 | Edited by Lisa | Moved edition to primary work. |
June 29, 2019 | Created by MARC Bot | Imported from Internet Archive item record |